There's a formula for solving a Quadratic Equation that has $x$ as a variable; e.g:
$$2x^2 + 5x – 8x = 0$$
Step 1 (is to find delta/discriminant):
$\Delta = b^2 – 4ac$
Step 2 (is to find $x_1$ and $x_2$):
$x$ = $\dfrac{-(b) \pm \sqrt\Delta}{2a}$
My question is… Is it possible to solve an equation which has $x$ & $y$ variables, with the formula above? Or is there another formula for equations with $x$ & $y$ variables?
Example:
$$2x^2 + 5xy – 8y^2 = 0$$
Best Answer
Going off of @lioness99a's comment, for your example you can set $a=2$, $b=5y$, and $c=-8y^2$ to get
\begin{align*} x &= \frac{-5y \pm \sqrt{(5y)^2 - 4\cdot 2 \cdot (-8y^2)}}{2\cdot 2} \\ &= \frac{-5y \pm \sqrt{89}|y|}{4} \\ &= \frac{1}{4} (-5 \pm \sqrt{89})y \end{align*}
or fix $x$ and treat $y$ as the variable.